A driving device (10) has a first speed change mechanism (30) receiving the mechanical power from an engine output shaft (8) by the first input shaft (27), a second speed change mechanism (40) receiving the mechanical power from the engine output shaft (8) and a motor (50) by the second input shaft (28), and a first clutch (21) which can connect the engine output shaft (8) and the first input shaft (27). When cranking an internal combustion engine (5), an ECU (100) selects the shifting step of the first speed change mechanism (30) and the second speed change mechanism (40) such that a mechanical power received by the second input shaft (28) is transmitted to the first input shaft (27) while being decelerated, and brings the first clutch (21) into connection state. A mechanical power from the motor (50) is decelerated by the second speed change mechanism (40) and the first speed change mechanism (30) in order to increase the torque and then transmitted to the engine output shaft (8) through the first clutch (21).